GATE Papers >> Mechanical >> 2015 >> Question No 242

Question No. 242 Mechanical | GATE 2015

Ratio of solidification time of a cylindrical casting (height=radius) to that of a cubic casting of side two times the height of cylindrical casting is________


Answer : 0.5 to 0.6


Solution of Question No 242 of GATE 2015 Mechanical Paper

Solidification time $t_s=k\;(^v/_A)^2$

For cylinder 

$t_{s1}=k\left(\frac{\mathrm{πr}^2\mathrm h}{2\mathrm{πr}^2+2\mathrm{πrh}}\right)^2$

now h=r

$=k\left(\frac{\mathrm{πr}^3}{2\mathrm{πr}^2+2\mathrm{πr}^2}\right)^2=k\left(\frac{\mathrm{πr}^3}{4\mathrm{πr}^2}\right)^2=k\left(\frac r4\right)^2$

For cube of side = 2h=2r

$ts_2=k\left(\frac{a^3}{6a^2}\right)=k\left(\frac a6\right)^2=k\left(\frac{2r}6\right)^2=k\left(\frac r3\right)^2$

$\therefore\frac{ts_1}{ts_2}=\frac{\left(r/4\right)^2}{\left(r/3\right)^2}=\left(\frac34\right)^2=0.5625$

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